Docker is helpful, but won’t be perfect since there’s no built-in migration. You’ll have to move any mounted directories like config and data and stuff. Docker is designed to be able spin up and down constantly, so it doesn’t really hold any persistent data in the image itself.
Also, I know you want free, but have you considered unraid? If you really need free you can try truenas or freenas or whatever, but a user friendly linux distro isn’t usually going to be too much overhead. I’d highly recommend unraid as a good option for users who need an easier way to work with all of their containers but don’t want to go as far as setting up a kubernetes cluster or something.
What he said ^. There’s no automation, you just have to make sure you catch everything is all. I may have made it sound more difficult than I intended, sorry about that!